Statistics

Lectures: Tue, Thus 2:30 - 4:00. SAS 204
Instructor: Shashi Prabh
Prerequisites: MAT202 Probability and Random Processes (or equivalent), Ability to write code

Introduction and course objectives

This course will introduce some of the fundamental concepts of statistics and statistical methods. One of the goals of this course is to discuss applications of statistical methods to solve real-world problems.

The course is organized into three parts. The first part introduces descriptive statistics, probability, distributions and convergence of random variables. The second part introduces sampling and experiment design. The third part introduces inference and learning from data where it covers topics such as parametric inference, hypothesis testing, statistical learning, regression and classification. The course will have two projects where the first project gives the students a taste of real-world data collection and statistical analysis, and the second project gives experience with statistical learning using real-world datasets. Students will use software to implement and experiment with the concepts taught in the course.

Learning outcomes
The students will be able to:

• Select and apply appropriate statistical method to a given real-world problem
• Use R or Python for data analysis
• Gain understanding of the statistical principles that are the basis of machine learning (learning from data)

Course content
Introduction, descriptive statistics , Probability, Bayes theorem and applications, Random variables, Distributions, Marginals, Multivariate distributions, Expectations, MGFs, Convergence of random variables, WLLN, Central limit theorem, Sampling theory, Confidence intervals, Experiment design, Parametric inference, Hypothesis testing, Comparing two populations , Statistical learning, Linear regression, Logistic regression, LDA, KNN.

Books

• Statistics, Freedman, Pisani and Purves, 4th edition, W. W. Norton, 2014
• All of statistics, Wasserman, Springer, 2003
• An Introduction to Statistical Learning with Applications in R, James, Witten, Hastie and Tibshirani, Springer, 2017
  Authors have made the book available online here.
• An Introduction to R, Venables and Smith, available online at: https://cran.r-project.org

Grading

• Quizzes (2): 10%
• Assignments: 5%
• Project: 10%
• Midterm exam: 35%
• Final exam: 40%

Helpful Advice ( a.k.a. expectation from the students! )
Pay attention and take notes! Get doubts cleared during the lecture itself -- do not hesitate to ask questions in class. Before attending a lecture, review your notes and scan the portion of the textbook that will be covered (see the course calendar page here). Do assignments on your own. If you happen to miss some session(s), do talk to someone else who attended or the TA to find out the topics covered and any announcement made.

Links
Course calendar
Course policies